RESEARCH AREA. Basic neuroscience involving structure/function relations for such neuronal structures as synapses, dendritic branching, and dendritic spines (as well as neuron populations with cortical symmetry), and for such functions as synaptic transmission, amplification and dendro- dendritic interactions in the context of spatio-temporal input patterns, logical processing of input, and neural plasticity, as in conditioning and learning. RATIONALE. To combine experimental data from neuroanatomy and from electrophysiology with biophysical models of nerve membrane (passive, synaptic and excitable) into a comprehensive theory which can lead to new insights and to testable theoretical predictions (which can, in turn, be used to design better experiments), it was necessary to create, explore and test mathematical and computational models (of increasing complexity). METHODOLOGY. Our methods include both analytical solutions and computational solutions of boundary value problems (involving partial differential equations) in the tradition of classical physics. They include also formulation and solution of problems in terms of systems of ordinary differential equations; when this is done explicityly for a compartmental model of a neuron, it is possible to accomodate a remarkable variety of dendritic branching and non-uniform distributions of membrane properties and synaptic inputs. RESULTS. Earlier results are summarized in Chapter 3 of "The Handbook of Physiology: The Nervous System, Vol. 1", Kandel, Brookhart, & Mountcastle, eds,; American Physiological Society (1977). More recent results are described in Chapter 22 of "Synaptic Function"; Edelman, Gall & Cowan, eds.; Wiley (1987).